SHTools: Tools for Working with Spherical Harmonics

Geophysical analyses are often performed in spherical geometry and require the use of spherical harmonic functions to express observables or physical quantities. When expanded to high degree, the accuracy and speed of the spherical harmonic transforms and reconstructions are of paramount importance. SHTools is a time and user-tested open-source archive of both Fortran 95 and Python routines for performing spherical harmonic analyses. The routines support all spherical-harmonic normalization conventions used in the geosciences, including 4p-normalized, Schmidt seminormalized, orthonormalized, and unnormalized harmonics, along with the option of employing the Condon-Shortley phase factor of ð21Þ m. Data on the sphere can be sampled on a variety of grid formats, including equally spaced cylindrical grids and grids appropriate for integration by Gauss-Legendre quadrature. The spherical-harmonic transforms are proven to be fast and accurate for spherical harmonic degrees up to 2800. Several tools are provided for the geoscientist, including routines for performing localized spectral analyses and basic operations related to global gravity and magnetic fields. In the Python environment, operations are very simple to perform as a result of three class structures that encompass all operations on grids, spherical harmonic coefficients, and spatiospectral localization windows. SHTools is released under the unrestrictive BSD 3-clause license.